The singularity theorems [1]}, [2]}, [3]} are some of the important aspects of general relativity. These have profound consequences in black hole mechanics, also known as black hole thermodynamics (BH). The singularity theorems are proved using the earlier work of Raychaudhuri [4]} in the causal structure of geodesic congruences, generalized in [5]}. However, proofs of singularity theorems in BH strongly depend on the null energy condition (see [6]}, [7]}, [8]}). The null energy condition essentially states that the energy-momentum tensor \(T_{\mu \nu }\)  of the matter satisfies the following condition
\(T_{\mu \nu }(x)n^{\mu }(x)n^{\nu }(x)\ge 0,\) 
